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Ocean, Earth & Atmospheric Sciences
2010
Modeling the Vertical Distributions of
Downwelling Plane Irradiance and Diffuse
Attenuation Coefficient in Optically Deep Waters
X. J. Pan
Richard C. Zimmerman
Old Dominion University, [email protected]
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Repository Citation
Pan, X. J. and Zimmerman, Richard C., "Modeling the Vertical Distributions of Downwelling Plane Irradiance and Diffuse Attenuation
Coefficient in Optically Deep Waters" (2010). OEAS Faculty Publications. Paper 117.
http://digitalcommons.odu.edu/oeas_fac_pubs/117
Original Publication Citation
Pan, X.J., & Zimmerman, R.C. (2010). Modeling the vertical distributions of downwelling plane irradiance and diffuse attenuation
coefficient in optically deep waters. Journal of Geophysical Research-Oceans, 115, 14. doi: 10.1029/2009jc006039
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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, C08016, doi:10.1029/2009JC006039, 2010
Modeling the vertical distributions of downwelling plane
irradiance and diffuse attenuation coefficient in optically
deep waters
Xiaoju Pan1,2 and Richard C. Zimmerman1
Received 8 December 2009; revised 25 March 2010; accepted 6 April 2010; published 17 August 2010.
[1] The diffuse attenuation coefficient (Kd) is critical to understand the vertical
distribution of underwater downwelling irradiance (Ed). Theoretically Ed is composed of
the direct solar beam and the diffuse sky irradiance. Applying the statistical results from
Hydrolight radiative transfer simulations, Kd is expressed into a mathematical equation
(named as PZ06) integrated from the contribution of direct solar beam and diffuse sky
irradiance with the knowledge of sky and water conditions. The percent root mean square
errors (RMSE) for the vertical distribution of Ed (z) under various sky and water conditions
between PZ06 and Hydrolight results are typically less than 4%. Field observations from
the southern Middle Atlantic Bight (SMAB) and global in situ data set (NOMAD) also
confirmed the validity of PZ06 in reproducing Kd. PZ06 provides an alternative and
improvement to the simpler models (e.g., Gordon, 1989; and Kirk, 1991) and an
operational ocean color algorithm, while the latter two kinds of models are valid to limited
sky and water conditions. PZ06 can be applied to study Kd from satellite remotely sensed
images and seems to improve Kd derivation over current operational ocean color
algorithm.
Citation: Pan, X., and R. C. Zimmerman (2010), Modeling the vertical distributions of downwelling plane irradiance and diffuse
attenuation coefficient in optically deep waters, J. Geophys. Res., 115, C08016, doi:10.1029/2009JC006039.
1. Introduction
[2] According to the Lambert‐Beer Law, underwater
downwelling plane irradiance [Ed (z)] decreases exponentially with depth (z):
Ed ð zÞ ¼ Ed ð0 Þ exp K d ð zÞ z :
ð1Þ
Equation (1) is wavelength dependent. For simplification,
the wavelength dependence is not shown for all equations in
this paper unless noted. K d (z) is defined as the average value
of the diffuse attenuation coefficient [Kd (z)] from the surface down to depth z, and represents an aggregate expression of the impact of the inherent optical properties (IOPs)
on radiance distribution. As such, it is often highly correlated with the concentration of optically active materials,
including phytoplankton, suspended sediments, and colored
dissolved organic matter (CDOM) [Gordon, 1989; Kirk,
1991, 1994; Mobley, 1994]. K d can be derived remotely
from empirical algorithms based on the blue‐to‐green ratio
of normalized water‐leaving radiance (nLw) or remote
sensing reflectance (Rrs) [Mueller, 2000; Signorini et al.,
1
Department of Ocean, Earth, and Atmospheric Sciences, Old
Dominion University, Norfolk, Virginia, USA.
2
Now at Research Center for Environmental Changes, Academia
Sinica, Taipei, Taiwan.
Copyright 2010 by the American Geophysical Union.
0148‐0227/10/2009JC006039
2003], and from quasi‐analytical algorithms based on the
relationships to IOPs measured in situ or simulated
[Gordon, 1989; Kirk, 1991, 1994; Mobley, 1994; Lee et al.,
2005; Wang et al., 2009]. The empirical algorithms do not
require detailed knowledge of bio‐optics, but they suffer
from large uncertainty and are insufficient for understanding
temporal or spatial variations in Kd(z). Quasi‐analytical
expressions based on water column optical properties often
improve generality of the empirical algorithms, but the
development of a simple and accurate derivation of Kd(z)
from IOPs remains elusive [Gordon, 1989; Kirk, 1994;
Mobley, 1994; Wang et al., 2009]. Although radiative
transfer models (RTMs), such as Monte Carlo simulations
and Hydrolight (copyright 1998–2001, C. Mobley, Sequoia
Scientific), provide “exact” solutions to predict Kd(z) from
IOPs, they are seldom applied to satellite remote sensing
since they are too complicated (time expensive by using
depth‐by‐depth simulations) to survey rapidly and routinely
for large areas. Moreover, RTMs cannot be inverted to
determine IOPs from the apparent optical properties (AOPs)
of remote sensing reflectance (Rrs) and Kd, which limits the
further application of RTMs in biogeochemical studies.
[3] Kd (z) is a relatively simple quantity to measure in situ,
but its relationship to coefficients of absorption (a), scattering (b), and backscattering (bb) is much more complicated
because Kd (z) is an apparent optical property (AOP) influenced by the angular structure of the submarine light field in
addition to the inherent optical characteristics of the medium
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[Kirk, 1994; Mobley, 1994]. The simplest form (named as
G89), provided by Gordon [1989] and valid only for limited
sky and oceanic conditions (e.g., medium solar zenith angle
and absorption‐dominant water), is often presented as:
Kd ¼ 1:0395
a þ bb
w
ð2Þ
Here w is defined as the average cosine of the incident
angle of direct solar beam just below the surface (w) after
accounting for refraction from the solar zenith angle (s) by
Snell’s Law [Kirk, 1994; Mobley, 1994]:
sinðw Þ ¼
sinðs Þ
1:34
ð3Þ
To make the equations simply, we assumed the vertical
distributions of IOPs are vertically homogeneous or can be
represented by their mean values from the surface to certain
depth. Gordon [1989] model does not account for the fact
that scattering typically causes Kd to increase asymptotically
with depth in most natural waters [Mobley, 1994], which
often causes it to overestimate Ed (z).
[4] Kirk [1991, 1994] derived a slightly more complicated
relationship from a series of Monte Carlo simulations:
Kd ¼
ða2 þ GabÞ
w
1=2
ð4Þ
Here G is a coefficient related to w and the shape of
scattering phase function. Unfortunately, constraining the
latter is so complicated as to make G extremely difficult to
parameterize, especially when the sun is not directly overhead. Kirk [1991] approximated that G = 0.425w − 0.19
and G = 0.473w − 0.218 in calculating the average Kd from
the surface down to the depth receiving 1% and 10% of
surface irradiance, respectively. Such approximations,
however, are not always appropriate for all water conditions,
especially for turbid coastal waters such as the Chesapeake
Bay estuary.
[5] More recently, Mobley [1994] summarized a two‐flow
model and presented a tantalizingly simple relationship
between Kd (z) and the IOPs:
Kd ð zÞ ¼
a þ bb
bb
Rð zÞ
d ð zÞ
u ð zÞ
ð5Þ
Here d and u represent the average cosines of downward
and upward plane irradiances, respectively, and R is the ratio
of upwelling plane irradiance (Eu) to downwelling plane
irradiance (Ed). Lee et al. [2005] developed a quasi‐analytical approach to Kd(z) based on equation (5) and the results of radiative transfer modeling, and rewrote it as:
Kd ð zÞ ¼ m0 ðzÞa þ vð zÞbb
a þ bb
d ð zÞ
Kd ðs ¼ 0 ; zÞ ¼ Kd ð1Þ
þ ½Kd ðs ¼ 0 ; 0Þ Kd ð1Þ expðPczÞ
ð7Þ
ð8Þ
The exponential slope (P) represents the vertical decay rate
of Kd (s = 0°, z) toward its asymptotic value in infinitely
deep water [Kd (∞)] along with the beam optical depth (x =
cz, where c represents beam attenuation coefficient).
However, Hydrolight simulations show that this asymptotic
closure model becomes invalid when solar elevation is low
(e.g., s > 40°). A more complicated model, such as a five‐
parameter asymptotic closure model expressed as the sum
of two exponential functions [McCormick, 1995], can
describe Kd (z) more accurately, but explaining the derived
parameters and estimating them from the IOPs and s
remain extremely difficult.
[7] In this paper, we developed a sufficiently accurate and
robust quasi‐analytical approach (named as PZ06) based on
the analysis of Hydrolight simulations to estimate Kd(z)
from measurable or derivable IOPs. This approach provides
a bridge to biogeochemical studies by inverse modeling of
IOPs and estimation of light availability reaching to the
floor. The calculations were verified against Hydrolight simulations and validated against in situ observations. PZ06
was also compared to the much simpler G89 model
(equation (2)), the Kirk [1991] model (equation (4) by using
the coefficients in calculating the average Kd from the surface to the depth receiving 1% of surface irradiance; named
as K91), and the operationally empirical algorithm (named
as S09; equation (9)) [Mueller, 2000; Signorini et al., 2003]
with the newly derived empirical coefficients in the Ocean
Color Reprocessing 2009 (http://oceancolor.gsfc.nasa.gov/
REPROCESSING/R2009/kdv4/).
ð6Þ
The parameterization of m0(z) and v(z), however, requires the
use of a lookup table (LUT) [Lee et al., 2005; Liu et al., 2002;
Morel and Gentili, 1993], which may not be appropriate for
all water masses. Since R is typically small in optically deep
water, the second term in the right side of equation (5) is often
ignored, leading to the common expression:
K d ð zÞ Hydrolight simulations show that the difference between Kd
calculated from equations (5) and (7) is typically less than 1%
for deep waters. This simple relationship of equation (7)
offers a potential solution to relate the vertical variation
of Kd and Ed to the IOPs, but the vertical distribution of d
and the method to estimate it are not well established.
Estimating d is more difficult than w because it includes
the angular distribution of sky radiance as diffracted by
airborne molecules and aerosols and water‐borne molecules and particles, in addition to the direct solar beam. It
is also explicitly variable with depth (z).
[6] An asymptotic closure theory has been developed
that describes the angular distribution of plane irradiance
as a function of depth (z) [Bannister, 1992; Berwald et al.,
1995; Zaneveld, 1989]. On the basis of this theory, the
vertical distribution of Kd at relatively high solar position
(e.g., s = 0°) can be expressed as:
K490 S09 ¼ 0:0166 þ 10a0 þa1 X þa2 X
2
þa3 X 3 þa4 X 4
ð9Þ
Here, X represents the ratio of remote sensing reflectance
(Rrs), X = log [Rrs (l1)/Rrs (l2)], and l1 and l2 are 490 and
555 nm for the Sea‐viewing Wide Field‐of‐view Sensor
(SeaWiFS). The derived coefficients a0, a1, a2, a3, and a4 are
−0.8515, −1.8263, 1.8714, −2.4414, and −1.0690, respectively. Finally, we applied PZ06 to estimate the distributions
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tion, along with equation (11), provides the average diffuse
attenuation coefficient of the direct solar beam:
1 1
K d ð zÞ direct ¼
z w
Zz
fKd ð1Þ þ ½a þ bb Kd ð1Þ expðPczÞgdz
0
ð12aÞ
The integration of equation (12a) results in the following
relationship:
K d ð zÞ
¼
direct
1
½a þ bb Kd ð1Þ
Kd ð1Þ þ
½1 expðPczÞ
w
Pcz
ð12bÞ
Thus, the relative vertical distribution of (Ed)direct is calculated as:
Figure 1. Dependence of the average cosines of downwelling irradiance on the solar zenith angle. Ed(0+) and
Ed(0−) indicate downwelling irradiance above and below
the surface, respectively. Calculations were based on Hydrolight simulations for clear sky.
of diffuse attenuation coefficient in the southern Middle
Atlantic Bight (SMAB) from satellite imagery.
2. Theory Behind PZ06
[8] The incident Ed entering the water column is assumed
to obey a constant transmission factor across the air‐sea
interface [0.98Ed(0+)] [Harding et al., 2005]. It is composed
of the direct solar beam [(Ed)direct] and the diffuse sky
irradiance [(Ed)diffuse] [Gordon, 1989; Kirk, 1994; Mobley,
1994]:
Ed ¼ ðEd Þdirect þðEd Þdiffuse
ð10Þ
If the fraction of the direct solar beam is defined as fdirect,
then the fraction of diffuse sky irradiance becomes (1‐fdirect).
[9] The direct solar beam, (Ed)direct, originating from the
solar zenith angle (s) is diffracted to w by Snell’s Law as it
crosses the air‐water interface [Mobley, 1994]. As with the
Gordon [1989] model, the diffuse attenuation coefficient of
the direct solar beam, [Kd(z)]direct, is assumed to vary
inversely with w:
½Kd ð zÞdirect ¼
½Kd ðw ¼ 0 ; zÞdirect
w
½Ed ð zÞdirect
Kd ð1Þ z ½a þ bb Kd ð1Þ
¼
f
exp
direct
Ed ð0 Þ
w Pc
w
½1 expðPczÞ
ð13Þ
The average cosine of the diffuse sky downwelling irradiance
above the water, [d (0+)]diffuse, is highly variable from 0.25
when the sun is nearly horizontal (s = 89°), in which condition irradiance arriving the water surface is almost diffused
and whose irradiance angular characteristics are similar to
those at cloudy or misty days, to 0.54 when the sun is directly
overhead (s = 0°) (Figure 1). Snell’s Law, however, constrains the inwater value of [d (0−)]diffuse to 0.69 when s =
89° and 0.78 when s = 0° (Figure 1). Exact radiative transfer
modeling has shown that the asymptotic value of the average
cosine of downwelling irradiance [d (∞)] in natural waters is
relatively constant at about 0.7 [Kirk, 1994; Mobley, 1994].
Thus, the vertical variation of [d (z)]diffuse ranges only from
∼0.78 to ∼0.7, and is relatively insensitive to both depth and
the solar zenith angle (s). Thus, the diffuse sky irradiance is
simply calculated as:
½Ed ð zÞdiffuse
Ed ð0 Þ
¼ ð1 fdirect Þ exp Kdiffuse z
ð14Þ
Equations (13) and (14) provide a general basis to determine
the relative vertical distribution of Ed (z):
Ed ð zÞ
Kd ð1Þ z ½a þ bb Kd ð1Þ
¼
f
exp
direct
Ed ð0 Þ
w
w Pc
½1 expðPczÞ þ ð1 fdirect Þ exp Kdiffuse z ð15Þ
ð11Þ
3. Application
Here, [Kd (w = 0°, z)]direct represents the diffuse attenuation
coefficient of (Ed)direct when the sun is directly overhead
(s = 0°, cos w = 1, w = 1), and closely approximates (a + bb)
at the surface (see equation (7)). [Kd (w = 0°, z)]direct
increases with depth as the direct solar beam is scattered by
water molecules and suspended particles. Application of the
asymptotic theory shown in equation (8) to describe the
vertical distribution of [Kd (w = 0°, z)]direct through integra-
3.1. Hydrolight Simulations
[10] Provided with the knowledge of IOPs (a, b, bb, and c)
and light field geometry (s and w), the unparameterized
variables in equation (15) include fdirect, Kd (∞), P, and Kdiffuse.
Hydrolight v4.2 was used here to derive the relationships
between these parameters and measurable or derivable water
and atmospheric properties (e.g., a, b, c, bb, s, cloud coverage, and so on). The default models and the input para-
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Table 1. Default Models and the Input Conditions for Hydrolight
Runs
Quantity
Range or Models
Atmospheric conditions
Sky model
RADTRAN [Gregg and Carder,
1990; Harrison and
Coombes, 1988]
Atmospheric pressure
1.013 × 105 Pa
Horizontal visibility
15 km
Relative humidity
80%
Precipitable water content
2.5 cm
Total ozone concentration
300 Dobson
Wind speed (WS)
5 m s−1
Solar zenith angle (s)
0° to 89°
Wavelength (l)
350 to 700 nm
Air mass type
Marine
Cloud coverage
0 to 100%
Water conditions (vertically homogeneous)
0.1 to 0.9
Single scattering albedo (w0)
0.005 to 0.5
Backscattering ratio (bb/b)
Scattering phase function
Petzold [1972] and Fourier‐Forand
function [Mobley et al., 2002]
Hydrolight default classic Case 1 IOP model
Pope and Fry [1997]
Water absorption (aw)
[Chl]
0 to 10 mg m−3
Particulate absorption (ap)
Prieur and Sathyendranath [1981]
Morel and Gentili [1991]
CDOM absorption (ag)
Smith and Baker [1981]
Scattering by pure seawater (bw)
Gordon and Morel [1983]
Particulate scattering (bp)
0.01833
Backscattering ratio (bbp/bp)
Scattering phase function
Petzold [1972]
meters used to calculate the atmospheric and water conditions are provided in Table 1. Values for the unparameterized
variables in equation (15) were derived from Hydrolight simulations using single scattering albedos (w0 = b/c) ranging
from 0.1 to 0.9 in interval of 0.1 and various scattering phase
functions including Petzold’s [1972] average (bb/b =
0.01833) and the Fournier‐Forand scattering phase function
(bb/b = 0.005 to 0.5) [Mobley et al., 2002].
[11] A special set of runs were calculated with s = 89°
(near horizontally), under which (Ed)direct approached zero.
Thus, Kdiffuse, which is almost independent of depth and s,
was directly calculated from the simulated results of Ed(z) at
s = 89° by the nonlinear least square match method of
TableCurve 2D v5.01 (SYSTAT Software Inc.). The water
column beneath the euphotic zone, defined as Ed(z)/Ed(0−) <
1%, was not considered in these simulations.
[12] Parameterizations of fdirect and Kd(∞) were calculated
directly from Hydrolight results. Kd(∞) depends only on water
IOPs, while fdirect is a function of the above‐water conditions
(here s and cloud coverage). [Ed(z)]direct was calculated from
equation (15) by subtracting the fraction of the diffuse source.
The exponential slope (P) was calculated from equation (12)
by nonlinear least square method from TableCurve 2D
v5.01 (SYSTAT Software Inc.). The relationships for these
four unparameterized variables were derived from full suite
of Hydrolight simulations as described above, and the results will be presented in detail in section 4.1.
[13] PZ06 (equation (15)) was also compared to Hydrolight simulations, G89 (equation (2)), and K91 (equation
(4)) by using typical Case 1 IOP conditions (Table 1).
Fidelity of PZ06 (equation (15)), G89 (equation (2)), or K91
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(equation (4)) (Ci) to Hydrolight (CHL) was evaluated by
calculating the percent root mean square error [(RMSE)i]
between their results.
X
1=2
1
2
ð RMSE Þi ¼
ðCi =CHL 1Þ
100%
n
ð16Þ
3.2. Global In Situ Data in Validating Kd Prediction
[14] The global in situ measurements from the NASA bio‐
Optical Marine Algorithm Data set (NOMAD; version 2.0a)
[Werdell and Bailey, 2005] were used to validate our
approach in predicting K d (z) down to 1 optical depth (K1oz,
where K1oz × z = 1). NOMAD includes coincident data set
of K1oz, chlorophyll a concentration ([Chl]), and bb. The
coincident near‐surface spectrophotometer (WET Labs,
Inc.) measurements of absorption coefficient (a), scattering
coefficient (b), and beam attenuation coefficient (c) were
downloaded from the SeaWiFS Bio‐optical Archive and
Storage System (SeaBASS). Finally, 115 stations, of which
75 from Plumes and Blooms cruises (PB) during January
2001 and February 2003, 21 from ACE‐Asia cruise during
March and April 2001 (RB‐01‐02), and 19 from the Japan–
East Sea cruise during July 1999 (JES‐1999), were included
in this paper [Werdell and Bailey, 2005]. The solar zenith
angle for each station based on the information of year, date,
time, longitude, and latitude was calculated from IDL codes
adopted from Ocean Color IDL library (http://oceancolor.
gsfc.nasa.gov/cgi/idllibrary.cgi). The sky was assumed to be
clear if no information of cloud coverage was provided.
PZ06 (equation (15)) was used to calculate K1oz by solving
equation (15) with the inputs of field IOPs and sky conditions. Model performance at selected wavelengths (412,
443, 490, 510, and 555 nm) was evaluated by the RMSE.
However, the obvious unmatched measurements defined as
Kd < a or Kd > 2(a + bb) were excluded for analysis in this
paper. The comparisons to G89 (equation (2)) and K91
(equation (4)), which were calculated from the inputs of
field IOPs and solar zenith angles, and the S09 operational
algorithm (equation (9)), which was calculated from the
field measurements of remote sensing reflectance (Rrs), were
also shown.
3.3. Validating the Vertical Distribution of Ed(z)/Ed(0−)
Against Field Observations in the SMAB
[15] Bio‐optical observations made in the southern Middle Atlantic Bight (SMAB) on 18 May 2005 were used to
validate the PZ06 (equation (15)) predictions of the vertical
distribution of Ed(z)/Ed(0−). The SMAB is well recognized
as typical river‐driven coastal waters where colored dissolved organic matter (CDOM) and detritus, along with
phytoplankton and pure water, contribute significantly to
bio‐optical properties [Mannino et al., 2008; Pan et al.,
2008]. The selected stations were located near Cape Henry
(Station 2; −75.88°W, 36.91°N) and ∼6.5 km east of the
Chesapeake Light Tower (Station 6; −75.64°W, 36.92°N).
Profiles of Ed(z) were collected with a HyperPro II hyperspectral radiometric system (Satlantic, Inc.) at 5 nm intervals
from 350 to 800 nm. Vertical profiles of absorption coefficient (a) and beam attenuation coefficient (c) were measured with an ac‐9 spectrophotometer (WET Labs, Inc.).
The scattering coefficient (b) was calculated as b = c − a.
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Figure 2. Vertical profiles of (a) absorption coefficient at 440 nm [a(440)] and beam attenuation coefficient at 440 nm [c(440)] and (b) backscattering coefficient at 443 nm [bb(443)] for Station 2 (−75.88°W,
36.91°N) and Station 6 (−75.64°W, 36.92°N).
Backscattering coefficient (bb) profiles were measured with
a Hydroscat‐6 (HOBI Labs, Inc.). All measurements were
averaged to 0.5 m depth bins except for the HyperPro
radiometer for which the records of Ed at the exact depth
points were used. To remove uncertain boundary effects
caused by high turbidity close to the seafloor or by touching
the seafloor with some instruments, all measurements were
at least 3 m above the seafloor. All data below the euphotic
zone, where Ed(z)/Ed(0−) < 1%, were excluded. Both stations were optically deep as <10% of Ed(0−) reached the
seafloor, even though their geometric bottom depths were
10 m and 21 m for Stations 2 and 6, respectively. Station 2
was more estuarine in character (surface salinity ≈ 22 psu)
and more turbid ([Chl] = 5.4 and 1.9 mg m−3 at surface and
bottom; higher a, c, and bb) (Figure 2). Station 6 was more
marine in character (surface salinity ≈ 28 psu) and less
turbid ([Chl] = 1.0, 0.6, and 1.1 mg m−3 at surface, middle,
and bottom; lower a, c, and bb) (Figure 2). The solar zenith
angles (s) of Stations 2 and 6 calculated from Hydrolight
simulations based on local date, time, longitude, and latitude
were 40.9° and 23.1°, respectively. Five common wavelengths (440, 488, 510, 555, and 676 nm) measured by the
ac‐9 and Hydroscat‐6 spanning almost the entire range of
photosynthetically active radiation (PAR; 400 to 700 nm)
were selected for analysis. Measurements at 488 nm were
assumed equal to those at 490 nm. As before, model performance was evaluated by RMSE.
3.4. Satellite Imagery
[16] The observations from SeaWiFS at the SMAB with
latitude from 36°N to 39.5°N and longitude from −77°W to
−74°W were processed from Level 1 to Level 2 using the
SeaWiFS Data Analysis System software (SeaDAS version
6.0), including the products of remote sensing reflectance
(Rrs), diffuse attenuation coefficient at 490 nm estimated
from equation (9) (K490_S09), and solar zenith angle (s).
Absorption coefficients of phytoplankton (aph) and CDOM
plus nonpigmented particles (adg) were estimated from
empirical algorithms based on Rrs ratios as described by Pan
et al. [2008]. The total absorption coefficient was then
calculated as a = aph + adg + aw, while the spectral
absorption coefficients of pure water were adapted from
Pope and Fry [1997]. Backscattering coefficients (bb) were
estimated by solving equation (17) [Gordon et al., 1988]
with satellite Rrs observations and the estimated absorption
coefficients (a).
2
Rrs ðÞ
bb ðÞ
bb ðÞ
0:0949
þ 0:0794
0:526
aðÞ þ bb ðÞ
aðÞ þ bb ðÞ
ð17Þ
The particulate backscattering coefficient (bbp) was then
estimated as bbp = bb − bbw. Scattering coefficients of pure
water (bw) were adapted from Smith and Baker [1981],
while forward and backward scattering was assumed isotropic resulting in bbw = 0.5bw. Particulate scattering coefficient (bp) was estimated from the relationships between bbp
and bp in this region as described by (X. Pan et al., manuscript in preparation, 2010):
SeptemberApril : bp ð490Þ
0:5
¼ 2:015 þ 4:061 þ 362:5bbp ð490Þ
MayAugust : bp ð490Þ ¼ 97:09bbp ð490Þ
ð18Þ
ð19Þ
Total scattering coefficient (b) was then estimated as b = bp +
bw, and beam attenuation coefficient (c) was calculated as c =
a + b.
[17] The sky was assumed to be clear for each pixel. The
average Kd(490) from the surface to one optical depth calculated from PZ06 model (K490_PZ06) by solving equation (15)
was compared to the results from S09 algorithm (equation (9)).
4. Results
4.1. Derived Coefficients
[18] On the basis of Hydrolight simulations (see the details in section 3.1), parameters containing in the PZ06
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Figure 3. (a) The relationships between the derived coefficients (g0 and g1) and solar zenith angle (s)
for a clear sky. (b) Dependence of the fraction of direct solar beam, fdirect, on cloud coverage. Simulated
results are indicated by data points connected by regression lines.
model (equation (15)) can be specified to the measurable
sky and water conditions. For clear sky conditions (e.g.,
cloud coverage <30%), the fraction of direct solar irradiance
(fdirect) was described by an exponential function of wavelength (r2 > 0.99, P < 0.001):
fdirect ð; clearÞ ¼ g0 þ g1 expð0:01Þ
The asymptotic diffuse attenuation coefficient [Kd (∞)] was
described by a second‐order polynomial function (r2 > 0.99
except when bb/b > 0.3 in which r2 > 0.97, P < 0.001):
Kd ð1Þ ¼ 1 D0 !0 D1 !20 c
ð24Þ
ð20Þ
Here g0 and g1 were significantly (r2 > 0.99, P < 0.001)
related to the solar zenith angle (s) (Figure 3a):
Here w0 is the single scattering albedo ( = b/c). D0 and D1 were
significantly (r2 > 0.99, P < 0.001) related to the backscattering
ratio (bb/b) (Figure 4):
g0 ¼ 1:147 0:363ðcos s Þ0:5
ð21Þ
D0 ¼ 0:959 2:346ðbb =bÞ0:5 þ0:747ðbb =bÞ
ð25Þ
g1 ¼ 19:25ð1 cos s Þ 7:26ðcos s Þ2
ð22Þ
D1 ¼ 0:046 þ 1:807ðbb =bÞ0:5 0:888ðbb =bÞ
ð26Þ
When cloud coverage was over 30%, fdirect became independent of wavelength (l) and s, but was significantly (r2 >
0.99, P < 0.001) related to the cloud cover (%cloud) (Figure 3b):
fdirect ðcloudyÞ ¼ 0:7 1 %cloud 2
Similar to Kd (∞),the diffuse attenuation coefficient of the diffuse
incident beam (Kdiffuse) was described by another polynomial
function (r2 > 0.99, P < 0.001):
ð23Þ
Figure 4. Dependence of the derived coefficients (D0 and
D1) on the backscattering ratio (bb/b). Simulated results
are indicated by data points connected by regression lines.
Kdiffuse ¼ 1:317 A0 !0 A1 !20 c
ð27Þ
Figure 5. Dependence of the derived coefficients (A0 and
A1) on the backscattering ratio (bb/b). Simulated results
are indicated by data points connected by regression lines.
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Figure 6. Dependence of the derived coefficients (B0 and
B1) on the single scattering albedo (w0). Simulated results
are indicated by data points connected by regression lines.
Similarly A0 and A1 were significantly (r2 > 0.99, P < 0.001)
related to the backscattering ratio (bb/b) (Figure 5):
A0 ¼ 1:399 1:012ðbb =bÞ0:5 0:939ðbb =bÞ
ð28Þ
A1 ¼ 0:047 þ 0:244ðbb =bÞ0:5 þ 1:120ðbb =bÞ
ð29Þ
The exponential slope (P) describing the vertical variation of
Kd(w = 0°, z) was significantly (r2 > 0.95, P < 0.001) related to
the backscattering ratio (bb/b):
P ¼ B0 þ B1 ðbb =bÞ0:5
ð30Þ
Here the coefficients B0 and B1 were significantly (r2 > 0.99, P <
0.001) related to the single scattering albedo (w0) (Figure 6):
B0 ¼ 0:817 0:877!0:5
0
ð31Þ
B1 ¼ 0:193 þ 0:421!0 þ 0:741!20
ð32Þ
4.2. Verification Against Hydrolight Simulations
of Ed(z)/Ed(0−)
[19] The parameter values derived from Hydrolight simulations were applied to equation (15) to calculate Ed(z)/
Ed(0−). In general, PZ06 (equation (15)) yielded estimates
that were within 2 to 4% RMSE of the Hydrolight simulations for a wide range of [Chl] and s (Figure 7a). Model
accuracy decreased as the water column optical density
increased (e.g., more particles and [Chl]) (Figure 7a). There
was no consistent relationship with solar zenith angle
(Figure 7a). G89 model (equation (2)) predicted Ed(z)/Ed(0−)
with an RMSE just below 10% for clearer waters (e.g., [Chl] <
1 mg m−3), and rose to nearly 80% as optical density
increased (e.g., [Chl] = 10 mg m−3) (Figure 7b). Under particle‐rich conditions, the G89 model (equation (2)) became
increasingly sensitive to solar zenith angle (Figure 7b)
because increasing s increased the fraction of the diffuse
Figure 7. The root mean square error (RMSE) of Ed(z)/
Ed(0−) for (a) PZ06 (equation (15)), (b) G89 model
(equation (2)), and (c) K91 model (equation (4)) against
Hydrolight simulations generated from the inputs of water
condition as described in Table 1. Symbols indicate s
ranging from 0 to 70° and averaged for all wavelengths
(350–650 nm) for each s. Water IOPs were Case 1 with
[Chl] = 0.01 to 10 mg m−3 for a 10 m water column. Solid
lines: average RMSE for all solar zenith angles and all
wavelengths.
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Figure 8. The RMSE of model performance in estimating Ed(z)/Ed(0−) within the layer of (a) Ed(z)/
Ed(0−) > 0.5, (b) 0.3 < Ed(z)/Ed(0−) < 0.5, (c) 0.1 < Ed(z)/Ed(0−) < 0.3, and (d) 0.01 < Ed(z)/Ed(0−) <
0.1 for the models of PZ06 (equation (15)), G89 (equation (2)), and K91 (equation (4)) against Hydrolight simulations generated from the inputs of water condition as described in Table 1. Symbols indicate
for [Chl] = 0 to 10 mg m−3 and for all wavelengths (350–650 nm).
incident solar beam whose diffuse attenuation coefficient
(Kdiffuse) was less sensitive to depth. Both depending on the
statistical analyses of radiative transfer simulations, Kirk
[1991] model (K91; equation (4)) showed similar RMSE to
our approach (2.65 ± 0.79% versus 2.44 ± 0.69%) for relatively
low particle conditions (e.g., [Chl] ≤ 1 mg m−3), but a little
higher RMSE (4.58 ± 1.88% versus 3.39 ± 1.04%) for relatively optically turbid waters (e.g., [Chl] = 3 and 10 mg m−3)
because of the impact of increasing scattering on radiative
distributions (Figure 7c). PZ06 model (equation (15)) is
competitive to G89 (equation (2)) or K91 (equation (4))
models, regardless of the optically upper layer (e.g., above
the depth receiving 30% of surface irradiance) or optically
lower layer (e.g., between the depths receiving 30% and 1%
of surface irradiance) (Figures 8a–8d). In general, all of
these three models increase their relative errors in reproducing Ed(z)/Ed(0−) as the increase of optical depth, especially
for G89 model (equation (2)) (Figures 8a–8d). Although
K91 model (equation (4)) performs similar RMSE to our
model, its relative higher errors in producing Ed(z)/Ed(0−) for
the optically upper layer (Figures 8a–8d), however, will
cause much higher absolute errors of Ed(z)/Ed(0−) for the
optically upper layer.
4.3. Validation Against NOMAD In Situ
Observations of K490
[20] All of four models, PZ06 (equation (15)), G89
(equation (2)), K91 (equation (4)), and S09 (equation (9)),
reproduced K490 well, as compared to global in situ observations (Figure 9). The RMSE for PZ06 (equation (15))
was 15.6% at 490 nm, as compared to 14.9%, 22.2%, and
15.4% from G89 (equation (2)), K91 (equation (4)), and S09
(equation (9)) models. S09 model (equation (9)) seemed to
produce K490 well at clearer water condition (e.g., K490 <
0.15 m−1), while tended to contain more uncertainty at more
turbid water condition (Figure 9). Compared to the original
performance of the operational algorithm by Mueller [2000],
Figure 9. Comparisons of the average diffuse attenuation
coefficient from surface to 1 optical depth at 490 nm
(K490) between NOMAD in situ measurements and estimations from PZ06 (equation (15)), G89 (equation (2)), K91
(equation (4)), and S09 (equation (9)) models.
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Figure 10. Comparisons of Ed(z)/Ed(0−) for Station 2: HyperPro observations compared with (a) Hydrolight simulations and estimates by (b) PZ06 (equation (15)), (c) G89 (equation (2)), and (d) K91
(equation (4)) models. (e) Comparison between Hydrolight simulations and PZ06 (equation (15)) estimates. For each symbol, comparisons for multiple depths from the surface to the depth with 1% of surface
irradiance were shown.
the coefficient of 0.016 in S09 (equation (9)) was intentionally embedded to reduce the underestimation of K490 for
clear waters. Such an intention, however, increases more
uncertainty in estimating K490 for more turbid waters
(Figure 9). G89 model (equation (2)) had typically lower
estimation of K490 than PZ06 (equation (15)) since it did not
consider the scattering effect (Figure 9). K91 model
(equation (4)) had typically higher estimation of K490 than
the field measurements and those from our model (Figure 9).
Part of the difference may be accounted by the expressions
of K490 from different models used in Figure 9: NOMAD
and PZ06 (equation (15)) calculated the average K490 within
one optical depth (from the surface to the depth receiving
∼37% of surface irradiance), while K91 (equation (4)) calculated the average K490 within the euphotic layer (from the
surface to the depth receiving 1% of surface irradiance). The
modification of K91 (equation (4)) with the coefficients to
calculate the average K490 within the layer receiving >10%
of surface irradiance, however, did not improve the performance of K91 (equation (4)) as compared to NOMAD
measurements. It suggests that a lookup table giving the
coefficients of equation (4) may be necessary to calculate
the average Kd within different optical depth. Although in
this case the performance from our model did not show
significant improvement from the other three models, the
validation results among these four models, however, should
be applied with caution. The field data in Figure 9 were in
fact part of observations used to develop the S09 algorithm
(equation (9)). Since most data points from this in situ data
set were from relatively clear water condition (e.g., 90% of
data was from waters with [Chl] < 3 mg m−3 and 60% of data
from waters with [Chl] < 1 mg m−3), PZ06 (equation (15))
showed no significant improvement from G89 (equation (2)),
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Figure 11. Comparisons of Ed(z)/Ed(0−) for Station 6: plots (a)–(e) were same to those in Figure 10. For
each symbol, comparisons for multiple depths from the surface to the depth with 1% of surface irradiance
were shown.
K91 (equation (4)), or S09 (equation (9)) because these three
models proved to work well in such conditions (Figure 7).
4.4. Validation Against Field Observations of Ed(z)/
Ed(0−) in the SMAB
[21] In the coastal waters of the SMAB, both Hydrolight
and PZ06 (equation (15)) reproduced the field observations
better than the G89 (equation (2)), based on RMSE calculations at both Station 2 (Figures 10a and 10b) and Station 6
(Figures 11a and 11b). Without accounting for the scattering
effect, G89 (equation (2)) tended to overestimate Ed(z)
(Figures 10c and 11c). Although K91 (equation (4)) produced similar RMSE results as Hydrolight and PZ06
(equation (15)), it seemed to underestimate Ed(z) for the
optically upper layer (Figures 10d and 11d). Such underestimations were also consistent with the general performance of overestimating Kd (z) from NOMAD observations
(Figure 9). After considering the relative difference between
the HyperPro profiles (e.g., 5% and 6% of standard devia-
tion at 676 nm for 3 profiles in Stations 2 and 4 profiles in
Station 6), and the additional unqualified error caused by
small‐scale horizontal variability in water column optical
properties (e.g., HyperPro was at least 20 m away from the
ship to avoid the effects of ship shadow on radiance and
AOPs, while ac‐9 and HS‐6 were profiled just beside the
ship because these IOP measurements were not affected by
ship shadow), the RMSE of 10% to 15% may be reasonable.
RMSEs between PZ06 (equation (15)) and Hydrolight simulations were 6.4% and 2.8% for Station 2 and Station 6,
respectively (Figure 10e and Figure 11e).
4.5. Spatial Distribution of Kd Derived
From SeaWiFS Imagery
[22] Figure 12 showed examples of SeaWiFS images of
K490_PZ06 for a winter date (3 November 2005,
“2005307”) and a summer date (12 May 2006, “2006132”)
in the SMAB. These images showed K490 estimated from
PZ06 (equation (15)) (K490_PZ06) decreased away from the
coast, and particularly from the Chesapeake Bay mouth, out
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Figure 12. Sea‐viewing Wide Field‐of‐view Sensor spatial
distribution of the average diffuse attenuation coefficient
from the surface to 1 optical depth at 490 nm estimated from
PZ06 (equation (15)) and S09 (equation (9)) for a winter
date (3 November 2005, “S2005307”) and a summer date
(12 May 2006, “S2006132”) in the southern Middle Atlantic
Bight. The distribution of the ratio between these two
models (S09/PZ06) is also shown.
toward the Atlantic Ocean. The primary frontal zone along
Virginia/Carolina coast [Sletten et al., 1999] and the mixing
of clear Gulf Stream waters with relatively turbid outflow
waters were also evident. The derived values of K490_PZ06
for these images were consistent with typical in situ measurements. For instance, the field measurements conducted
on 18 May 2005 showed surface Kd(490) decreasing from
∼0.5 m−1 at near Cape Henry to ∼0.15 m−1 at the east of the
Chesapeake Light Tower, similar to the values displayed for
“2006132” (Figure 12). Although the distribution of K490
estimated from S09 (equation (9)) (K490_S09) appeared
qualitatively similar to our approach, the ratio of K490_S09
to K490_PZ06 indicated regions where these two approaches
differed considerably. Without considering the Chesapeake
Bay and Delaware plume regions, this ratio typically increases
from 0.55–0.7 on the inner shelf to 0.7–0.85 on the middle
shelf, and becomes more agreeable (0.85–1.1) toward offshore as waters become clearer, especially during summer
(Figure 12). Such a trend was consistent with other works
using the old versions of the operational algorithm, which
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showed significant underestimations of the diffuse attenuation coefficient in turbid waters (e.g., a factor of 2–3 in the
Chesapeake Bay) [Mueller, 2000; Signorini et al., 2003;
Wang et al., 2009]. The ratio of K490_S09 to K490_PZ06,
however, is typically very close to 1 (e.g., 0.9–1.1) for the
Chesapeake Bay plume region and the Delaware Bay
(Figure 12). The different performance of the ratio between
these two models can be due to the components contributing
to the bio‐optical properties. On the outer shelf and the open
waters, CDOM is the dominant contributor (e.g., 50–70% at
443 nm) to the absorption [Pan et al., 2008]. Since CDOM
is a nonscattering source [Mobley, 1994], the adding consideration of scattering impact from PZ06 (equation (15))
shows no significant improvement from the operational
algorithm for the outer shelf and open waters (Figure 12).
The NOMAD comparisons showed that the ratio of S09
(equation (9)) to the field measurements for the stations
whose CDOM accounted for >50% of absorption at 443 nm
was close to 1 with the mean ±SD of 0.993 ± 0.292 (N =
237). On the inner shelf, however, particles (phytoplankton
plus nonpigmented particles) play increasing important role
on the bio‐optical properties [Pan et al., 2008]. The performance of S09 (equation (9)) then depends on, at least
partly, the relative component concentrations of phytoplankton (typically larger size with lower backscattering
ratio to scattering) and nonpigmented particles (typically
smaller size with higher backscattering ratio to scattering).
The NOMAD comparisons showed that the ratio of S09
(equation (9)) to the field measurements for the stations
whose CDOM accounted for <50% of absorption at 443 nm
was close to 1 with the mean ±SD of 1.048 ± 0.429 (N =
408) for the stations whose nonpigmented particles accounted for <50% of particulate absorption at 443 nm, and
decreased to 0.700 ± 0.477 (N = 60) when contribution from
nonpigmented particles increased. The data used in Pan et al.
[2008] showed that the contribution from nonpigmented
particles to particulate absorption decreased as the increase of
pigments, or lower ratio inside the Chesapeake Bay and the
plume region. The S09 (equation (9)) products, thus, agreed
better to PZ06 (equation (15)) for the Chesapeake plume
region than for other inner shelf region (Figure 12). Since the
phytoplankton growth in the lower Delaware Bay, in contrast
to the lower Chesapeake Bay, is subject to light availability
rather than nutrients [Harding et al., 1986; Marshall and
Alden, 1993], the contribution from nonpigmented particles
to particulate absorption is higher than that in the lower
Chesapeake Bay [Pan et al., 2008]. The S09 (equation (9))
products then showed typical lower values than PZ06
(equation (15)) in the lower Delaware Bay (Figure 12). In
summary, our approach may imply an improvement to estimate K490 for turbid water as compared to S09 (equation (9)),
especially for regions with higher sedimentary resuspension.
[23] Figure 13 showed the time series comparisons of
Kd(490) derived from S09 (equation (9)) and PZ06
(equation (15)) for three selected stations along the Chesapeake Bay estuary during 2005. Station (Stn) A (−75.88 W,
36.91°N) represents a station on the inner shelf influenced
significantly by the river discharge, while Stn B (−75.64°W,
36.92°N) and Stn C (−74.50°W, 36.50°N) represent stations
on the middle shelf and outer shelf. The derivations from
S09 (equation (9)) were generally lower than those from
PZ06 (equation (15)) and more agreeable to each other for
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Figure 13. Time series of the diffuse attenuation coefficient [Kd(490)] estimated from S09 (equation (9)) and
PZ06 (equation (15)) for three selected stations during 2005.
(a) Station (Stn) A (−75.88°W, 36.91°N), (b) Stn B (−75.64°
W, 36.92°N), and (c) Stn C (−74.50°W, 36.50°N) represent
stations on the inner, middle, and outer shelf, respectively.
(d) The ratio of S09/PZ06.
those regions with less impacts from river discharge, e.g., the
ratio (S09/PZ06) increasing from the middle shelf (81.3 ±
8.8%) to the outer shelf (92.8 ± 7.1%) (Figure 13). The ratio
(S09/PZ06) was more variable on the inner shelf (84.1 ±
15.7%) (Figure 13) as the increase of impact from the river
discharge. Such results agreed with the analyses for the
spatial distributions of the diffuse attenuation coefficients
estimated by these two models (Figure 12).
5. Discussion
[24] Unlike the empirical algorithm derived from ratios of
Rrs optical bands [Mueller, 2000; Signorini et al., 2003],
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PZ06 (equation (15)) is based on a radiative transfer analysis
that provides a robust but quasi‐mechanistic relationship
between Kd(z) and IOPs although the derivation of IOPs
could be empirical (e.g., the application of our model to the
SMAB region). Thus, it overcomes the uncertainty by the
empirical algorithm (S09 or equation (9)), especially when
the in situ data set does not cover whole range of water
condition. In general, PZ06 (equation (15)) provides the
same accuracy level for all water conditions, while S09
(equation (9)) has lower capability in very clear water and
more turbid water conditions [Mueller, 2000; Signorini et
al., 2003]. Although the simple formations of G89
(equation (2)) has been applied widely to bio‐optics, its
shortcoming in significantly underestimating Kd(z) without
considering the scattering effect is obvious (Figures 10 and
11), especially in particle‐rich water conditions. Kirk [1991]
model (K91, or equation (4)), in the other way, is subject to
the difficulty to parameterize the appropriate coefficients
related to scattering phase function. Since most of field data
from the adapted NOMAD data set were collected from
waters with medium particles (e.g., 90% of stations whose
[Chl] < 3 mg m−3) and medium solar positions (e.g., 83% of
stations whose s < 60°), the validation performance from
PZ06 (equation (15)) did not show significant improvement
from G89 (equation (2)), K91 (equation (4)), or S09
(equation (9)). Limited field data from Case 2 waters (e.g.,
the southern Middle Atlantic Bight) and Hydrolight simulations, however, proved that significant improvement in
estimating Kd from our algorithms may be accomplished
over the other models.
[25] The “exact” radiative transfer models (RTMs; e.g.,
Hydrolight) provide very useful tool in studying inwater
bio‐optical characteristics for individual stations, but they
are not suitable to inversely derive AOPs or IOPs from
satellite remote sensing observations. The application of
RTMs or PZ06 (equation (15)) to derive Kd from satellite
remote sensing depends on satellite‐derived IOPs. The
running times of RTMs to calculate Kd from IOPs, however,
are typically very expensive, which limits their applications
to process satellite images. PZ06 (equation (15)), in contrast,
based on the statistical results of RTM simulations, provides
an operational and quick method to obtain Kd from satellite‐
derived IOPs with reasonable and robust accuracy.
Although more complicated than G89 (equation (2)), K91
(equation (4)), and S09 (equation (9)) performance, the
improvement of computer capability will overcome the
requirement of complicate calculations in accurately estimating the important bio‐optical property, Kd. Expressed as
a simple equation, PZ06 (equation (15)) is also suitable to
apply to further bio‐optical studies, e.g., in retrieving IOPs
for optically shallow water conditions, which is difficultly
solved by RTMs [Pan, 2007].
[26] PZ06 (equation (15)) assumes the water is optically
deep. When the water column is optically shallow, the
upwelling irradiance (Eu) originating from bottom reflectance and its second‐order contribution to Ed(z) need to be
assessed. Although such a contribution is relatively small in
the SMAB (usually <1% based on Hydrolight simulations),
it is not negligible in some extreme conditions (e.g., very
bright floor and very strong backscattering coefficient of the
Bahamas Banks) in which Eu generalized by bottom
reflectance may be >10% of Ed, especially near the seafloor.
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In the SMAB, in which the bottom reflectance (Rb) is relatively low (e.g., in general Rb < 0.1 [Pan, 2007]), the second‐order contribution of the bottom reflectance on Ed(z)
can be ignored. Thus, PZ06 (equation (15)) can be applied to
photosynthetic models for estimating water column primary
productivity [Behrenfeld and Falkowski, 1997; Behrenfeld et
al., 2005] and benthic optical environment from which seagrass primary productivity and distribution can be estimated
for the SMAB [Dierssen et al., 2003; Zimmerman, 2003].
[27] Since PZ06 (equation (15)) requires the detailed IOPs
to calculate Kd, the ability of the inverse model to retrieve
absorption, scattering, and backscattering coefficients is
critical. Unfortunately, the complicated condition in coastal
waters often causes some errors in retrieving IOPs. For
example, GSM01 model [Garver and Siegel, 1997;
Maritorena et al., 2002] requires the remote sensing
reflectance (Rrs) for all bands to be equally accurate, but
strong CDOM absorption and inadequate knowledge of
aerosol absorption and scattering often cause significant
underestimation of Rrs in the blue bands (e.g., 412 and 443
nm) [Bailey and Werdell, 2006; Siegel et al., 2000].
Therefore, the retrievals of IOPs in this study have to
depend partly on empirical algorithms [Pan et al., 2008]
before the validations of semianalytical retrievals can be
achieved.
6. Conclusion
[28] By dividing the incident solar beam into direct and
diffuse sky components and separating the analyses of their
vertical characteristics along the depth with the water depth
gradient, PZ06 (equation (15)) successfully reproduces both
the “exact” results of Hydrolight simulations and field observations of the vertical distribution of downwelling plane
irradiance [E d (z)]. It offers improvement over Gordon
[1989] simpler model (which works better for upper layer
than for lower layer), Kirk [1991] model (which works
better for lower layer than for upper layer), and an operationally empirical algorithm [Mueller, 2000; Signorini et al.,
2003] (which works better for clearer waters or turbid waters
whose bio‐optical properties dominated by CDOM or phytoplankton than for more turbid waters with relatively higher
fraction of particles from nonpigmented particles). However, the accuracy of this approach depends significantly on
the inverse retrieval of IOPs from Rrs, which may require
tuning for regionally specific parameters, especially in near‐
shore coastal waters.
[29] Acknowledgments. We thank David Ruble, Victoria Hill, Margaret Stoughton, and Jasmine Cousins for help with field observations and
comments on this manuscript. We are grateful to the help from the captain
and the crew of R/V Fay Slover. We also thank D. Siegel, G. Mitchell, and
all of their coinvestigators for releasing their SeaBASS data contributions
to the public. We thank the Editor (Des Barton), and Jeremy Werdell
and an anonymous reviewer for their thorough, thoughtful jobs and constructive comments. Financial support was provided by NASA (award
NNG04GN77G). Funding for Mitchell data collected during ACE‐Asia
and the Japan–East Sea cruises was provided by NASA SIMBIOS and
the Office of Naval Research, respectively.
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